Instrument for measuring the slopes of a curve



Juiy 1948' E. J. LUNNEY 2 9 INSTRUMENT FOR MEASURING THE SLOPES OF A CURV E Filed June 12, 1946 2 Sheets-Sheet 1 IN VEN TOR. fan 420 L AWEV 1/41 immw juiy 2?, 3948. E. J. LUNNEY 2,445,792

INSTRUMENT FOR MEASURING THE SLQPES OF A CURVE Filed June 12, 1946 l 2 Sheets-Sheet 2 32 1/ 50/7/9801 1 IVA-'7 Patented July 27, 19 48 INSTRUMENT FOR MEASURING THE SLOPES OF A CURVE Edward J. Lunney, Dayton, Ohio Application June 12, 1946, Serial No. 676,127

Claims. ((31. 88-74) (Granted under the act of March 8, 1883, as amended April 30, 1928; 370 0. G. 757) The invention described herein may be manuiactured and used by or for the Government for governmental purposes without payment to me of any royalty thereon.

This invention relates to an improved instru-' ment for measuring the slope of a curve at any point thereon.

In the past, this operation was done by many time consuming and inaccurate methods, among which was to draw a circle fitting the slope, drawing a tangent to the circle along the curve and then measuring the divergence of the tangent from a vertical reference line. One device for curve slope measurement is the subject of Patent 1,907,873 to Richards and Roope. It is upon devices of this sort that the present invention is an improvement in that it is faster, just as accurate and much more convenient.

Referring now to the drawings:

Fig. l is a perspective view of the device.

Fig, 2 is a sectional elevation taken on the line I 2--2 of Fig. 1.

Fig. 3 is a fragmentary detail in elevation of a pin which may be provided to center the device.

Fig. 4 is a perspective view of the device in use in determining the slope of a curve drawn on graph paper. Alignment has not yet been accomplished.

Fig, 5 is a perspective view corresponding to Fig.

7 4 with the difference that alignment of'the curve with it refiectionhas been performed.

In the drawings i0 is an outer base, the general shape of which is preferably square, although it may :be made circular or octagonal. In the center of base it, there is a large circular opening ll into which rotatably fits an inner base l2. An L-shaped overlapping joint l3, shown in Fig. 2 is used to provide an easy but accurate fit; Transparent thickplastic is the preferred material.

Two devices are used to prevent the inner base it from separating from the outer one it. The first device it is a small plastic block cemented to the upper surface of base it so that the block extends over the inner base it but is not cemerited thereto. The second device is a screw lock it which comprises a thumbscrew it threadedly engaging the base it near the outer edge of joint is. A disc ll of plastic which has been relieved on its inner surface, is held by screw it to the face of base iii and partially over base it so that when screw it is tightened, base it cannot be rotated except with difficulty. The setting of the two bases in relation to each other is thereby preserved.

Across the diameter of inner bas ii there are mounted a pair oi hinge blocks II in which are pivoted a second pair of hinge blocks It by means of pins 2%. Slots 2i are provided in base II to receive blocks i 9 upon their rotation.

A transparent mirror 22, preferably a "dark" mirror, is mounted in grooves 23 so that when blocks is and mirror is are upright, the lower edge of the mirror will be in the plane of the bottoms of bases it and it. a small dot it is s by scratching a little of the reflecting substance from the middle point of the lower edge oi the mirror so that the dot may serve as a fiducial point. As such, it defines the center of bases it and i2 and is the center of rotation oi base'it. A

tab it and guard 25 protect the top edge of mirror .as a reflection in the mirror. A second opening 28 is shown, the purpose of which is to provide space to swing the mirror about pins 20 and also for observation of curves from the reverse side or the mirror. For the measurement of slope, a scale 29 divided in minutes of angle is provided on the.

inner edge of base iii and a reference line In placed radially on inner base i! to reach the scale.

' readily be rotated with pin it as axis.

For convenience in carrying the instrument, the mirror may be folded down to a position shown in dotted lines on Fig. l.

The instrument is used as follows:

To measure the slope of the curve A at the point 0, the instrument is placed on the pawr it with the inner base it free to rotate. The index pin this placed directly on point 0. The outer base it is then rotated until its outer edges are each parallel respectively to the m and Y! axes on the graph paper ti on which the curve is drawn. The operator then looks through the mirror 22 as shown in Fig. 4 and sees the branch A0 of the actual curve A003 and also the reflected image 0A of the section 00 of the actual curve.

With the base ill still aligned with the X and &

' axes, the inner base 82 and the mirror .32 are rotated until the images A and A0 are super= considerable portion of their length The mirronsfi is now perpendicular posed for a (see Fig.

' to the tangent or the curve at Q and the index mark 80 and the scale it may be read to determine the slope of the curve with respect to the base line. A vernier may be added to provide more accurate readings.

In the event that it is desired to draw the actual tangent to the curve at O, a second point on the tangent may be located'by spotting through a small'holo 2i through the inner base I? at the index line til with a pin or sharp-pointed pencil.

The remaining space on the meeting edges of outer base it and inner base l2 not occupied by the degree scale may be used to bear a scale graduated in numerical values of the tangent func-' tion.

In an instrument of this character in which the circular scales are dispensed with, the slope of M (not shown) with the graph lines is found so that a segment of the flducial line will form the hypotenuse of a right triangle of which one vertical and one horizontal graph line are the remaining two sides. The line M is derived from a line drawn on the base of the instrument from the mirror 22 rto the outer edge or the base and is perpendicular to both the mirror and said outer edge. It is tangent to the reflected projection AO.

The slope of the section of the fiducial'line M maythen be determined by counting the unit graph lines to determine the tangent as a ratio of the side opposite to the side adjacent the an-.

gle that the section of line M makes with base line XX. 1

on the meeting edges of said bases for ascertaining their relative" positions, a transparent mirror mounted erectably within the inner base on a diameter thereof, said inner base having before and behind said mirror an opening of substantial length and breadth in said inner base whereby a curve drawn upon coordinate paper lying flat beneath said opening, said curve running to said mirror below said openings when the instrument is laid to rest upright on its bases will appear to be continued in said mirror and may be aligned with its reflection therein and its directly-observed actual prolongation, whereby the angular position of said mirror and inner base with respect to the outer base will indicate the slope of the tangent to the curve with respect .to the reference axes of the curve.

3. A geometrical instrument according to claim 2 having in addition hinged blocks between which .said mirror is pivoted and shoulders in the inner base against which the mirror abuts when erected, said shoulders being adapted to align said mirror vertically.

4. A geometrical instrument comprising a base, a transparent mirror mounted vertically in said base, a pin extending outwardly from the lower edge of said mirror at the middle point thereof and extendin down substantially to the surface upon which the instrument rests said base having a cutout portion before said mirror, whereby a curve drawn on a surface upon'which' the instrument rests upon its base may be aligned to continue through the point defined by said pin with its reflection in said mirror and the real prolongation of the curve imultaneously observed through said mirror upon rotation 01 the instrument.

5. A geometrical instrument adapted to determine the slope of a curve at any point thereon Certain omissions may bemade in the structure shown. The base may be simplified so that only the inner base remains and that need not be circular. It need have only the cut out portion 18 and a vertical block such as I 9 for holding the mirror 22 vertical. able, 1. e., the mirror can be permanently erect.

The invention claimed is: v

1. In a geometrical instrument, an outer base. a circular inner base rotatably mounted therein, indicia on the meeting edges of said bases for ascertaining their relative positions, a transparent mirror mounted vertically within the inner base on a diameter thereof, said inner base having an opening which extends before and behind said mirror whereby curves drawn on paper lying flat below said opening and running toward the mirror upon the surface of said paper upon which the instrument is laid .to rest on' its bases will appear to be continued in said mirror whereby the reflectionof a curve drawn upona paper surface upon which the instrument rests may be aligned by rotating the inner base and mirror with the actual prolongation of said curve observed directly through the mirror to obtain an indication from the position of said mirror and inner base with respect to the outer base, of the slope of the tangent to the curve.

2. In a geometrical instrument, an outer base,

Block is need not be mov- I which comprises a square outer base, a circular inner base 'rotatably mounted therein upon a stepped joint, indicia at the meeting edges of the two bases whereby their relative angular positions =may be determined, a transparent mirror erectably mounted on a diameter of said inner base, pivot blocks in which said mirror is pivotally mounted so as to be foldable downward and vertically alignable, said inner base having a keystone shaped opening in front of said mirror when the latter is erected and a U-shaped openingbehind it, a pair of aligning shoulders for said mirror to hold the mirror in erect alignment, said shoulders being between said openings, and means for retaining said inner base in said outer one and for locking said inner base against rotation.

EDWARD J. LUNNEY.

REFERENCES orran file of this patent:

UNITED STATES PATENTS Number FOREIGN PATENTS Number Country Date Germany Sept. 26, 1911 Great Britain May 18, 1942 

